Day 6

Today we revisit Graphing Stories and the MARS task Interpreting Distance-Time Graphs, but this time we will write linear equations for all the stories that have all linear components - even if they are piecewise.

The opener will review how to find the y-intercept when you aren't given it but, instead, are given the slope and a point, or more often two points and you have to calculate the slope first.

We will then discuss one of the student's homework screencasts from the previous class.

Today's lesson will work through the Activity Builder Graphing Stories Part 2. This will solidify our ability to connect descriptions, tables of values and graphs, and then to be able to write equations for those graphs (including domain restrictions for piecewise functions). As part of this we will need to utilize solving for the y-intercept since we won't always have that for the different pieces of our graph.

For homework they will complete one more graphing story and record a screencast with their thinking. The hope is that by the end of this lesson they are feeling very comfortable with everything related to graphing stories, including writing equations for linear data.

Day 5

Today I hope to to cement the connection between a situation, a table of values, the graph, and the equation. The will also begin to connect slope more explicitly with the idea of rate of change and specifically with speed for distance-time graphs.

We'll begin with an opener that reviews slope and connects it to rate of change and speed (screenshots below).

We'll then complete an activity that requires gathering some data on three people walking, entering it into an Activity Builder, then using the data to try to come up with equations to describe their motion. The first walker will start at 0 and walk at an even pace for 10 seconds. The second walker will start at 3 feet (for example) and walk at a steady pace (hopefully slightly different pace than the first walker, we'll see). The third walker will walk a piecewise graph. Starting at 2 feet (for example), walking at a steady rate for 4 seconds, standing still for 3, then walking at a steady rate back toward the starting point for 3 seconds.

The hope is that they will not only connect the actual walk to the data tables and the graph, but they'll get a better idea of how speed relates to the graph and the idea of a domain restriction and piecewise equations. In our next class we will then revisit Graphing Stories and the MARS activity, coming up with equations for any of the linear graphs (including the piecewise ones).

For homework students will take a piecewise table of values, graph it on Desmos and come up with equations, domain restrictions, and a verbal description of what may have happened, then record a short screencast of their thinking.

Day 4

Today we'll finish the MARS activity we started yesterday, looking at the connection between the tables of values, the graphs, and the verbal descriptions.

I'll use today's opener to again review slope-intercept form, see the screenshots below.

We'll then discuss one of the student's screencasts of last night's homework problem.

The lesson will continue with the MARS activity, matching the various tables of values to the graphs and verbal descriptions (slides, see the MARS activity for the tables of values we're using).

Today's homework will be to tie together the verbal description, the graph and the table of values, and again use a screencast to share their thinking about the problem.

My hope is that after today they are feeling fairly confident connecting descriptions to graphs to tables of values, and perhaps seeing the connection to rate of change and slope (although we'll make that more explicit in our next class, which is two days away because we don't meet on Thursdays).

Day 3

Today I want to continue exploring the relationship between two related variables, and how to sketch a graph given a verbal description. Today we'll focus on distance/time graphs by using this MARS activity.

I'm going to start with an opener that will hopefully remind them of what they already know about slope-intercept form of a linear equation. Again, in Formative, so I'll give you screenshots.

After discussing the opener, we will then view and discuss one of the screencasts they did for homework last night (the assumption being that at least a few of them were successful). We'll talk about the math in the problem, of course, but we'll also talk about problems anyone had with the screencast process and possible solutions.

We will then move on to the MARS task (outlined in the slides). The entire task is going to take one and a half to two class periods, so I'm anticipating getting through the "sharing posters" phase (bottom of page T-6 in the MARS pdf), then adding in the data tables tomorrow.

Their homework will be to complete the Journey to the Bus Stop activity, including recording and submitting a short screencast to describe their thinking. I again hope they will have the opportunity to start the homework in class and perhaps only have to do the screencast portion outside of class.

Day 2

Since my first day with my Algebra students is a Friday (their second day of school, but Algebra doesn't meet on Thursdays), I sort of feel like Day 2 is my "real" first day with students. My first unit is "Everything Linear", and I want to really hit hard the ideas of relation (and eventually function) and rate of change, while liberally sprinkling in modeling. While it's hard to tell exactly what my students will have had mathematically before me, most of them theoretically will already know how to solve equations, have learned about slope/rate of change, and already done quite a bit of graphing using slope-intercept. (I meet with that incoming 9th grader this Wednesday, so I may have to revisit this statement later this week.)

This day's opener is based on Dan Meyer's 3-Act Sugar Packets. Right now I'm experimenting with Formative and, since I'll be assigning it to my class, I can't link to it so that you can see it. Hopefully these screen shots will give you an idea.

I thought this was an interesting way to start and hopefully immediately engaging. In the past, I've used this as a lesson activity, so I do have some concern that it might be "too much" for an opener. (I also wish Formative allowed a "page break" so that students could enter their estimates, click next, then see the information necessary to solve it exactly; worried they'll scroll down before making estimates.)

Then I decided a great lesson to start with was a Desmos Activity Builder remix of Dan Meyer's Graphing Stories. (FYI - you will be seeing a lot of Desmos and Dan Meyer in subsequent posts.)

I really like how this gets students to think about the relation between two variables in an informal way, yet one that leads to more formal mathematics pretty nicely. Because Desmos recently added the ability to sketch, it fits nicely into Activity Builder. (They are apparently working on the ability to embed videos, right now I just link to them.) I'm reasonably happy with the way this worked out, but am still debating if including all 10 of them is too much. I scaffold the first two, asking them to stop after their sketches so that we can compare everyone's sketches, then turn them loose after that. I think that they'll be able to run with it, but not sure.

Their homework (which hopefully they will get to start on in class - I think I will cut the lesson short if I have to to make sure that happens), is to complete one more graphing story, then record a short screencast describing how they went about coming up with their solution. This will be their first attempt at a "production" screencast (if all goes well they will have practiced on Friday), and I'll make sure to let them know that if they have trouble at first, we'll work through it and that I expect by the end of the week everyone will be able to smoothly make screencasts. (Having the ability to come in on an unscheduled hour will be really helpful here for any students who are really struggling with the screencasts at first.)

This sounds like a great day in my head, but what are your thoughts? Would love to hear feedback, suggested tweaks, or alternatives. (Day 2 Slides)

Day 1

Our first day of school this year is Thursday, August 18th. My Algebra class doesn't meet on Thursdays, so my first day with them will be Friday, August 19th.

The class starts with announcements over the PA (we meet third period, which is when announcements are scheduled). As they enter the room (I'll greet them at the door) they'll see these slides displayed on the projector. They'll find their seats, listen to the announcements, and hopefully navigate to our class website just fine.

I won't go over Course Expectations (because most of them will hopefully have already read through them), but I will ask if there are any questions. I will then spend just a minute or two on "Fisch Philosophy" in terms of what I want them to get out of the course.

We will then sample all the tech, working through many of the things on the Setup page that they've hopefully already setup, with a big emphasis on helping each other, and generally just getting used to some of the tools we'll be using. While we're doing that, we'll experience a little math along the way, too. (I don't have the sample openers created yet in Kahoot and Formative, nor have I created the sample Activity Builder activity in Desmos, but all of those will be Algebra-related while learning the basics of how the tool works.) We will then create a sample screencast (not Algebra-related, but showing them how to get an image onto their screen that they will need to know for their homework problem each night). If we manage to successfully get through all of this, it will be amazing, but we'll give it a shot.

At the end of class there is a link to "Assignment 0" which is all of the things I suggested they do before school starts, but that is due in a week if they haven't finished some or all of it. Since our first day is a Friday, they'll have a weekend before I'll see them again, and then Monday will be a more "typical" day.

While I wish there was a bit more mathematics on this first day, I'm worried that the tech could be overwhelming so I want to expose them to as much of it as possible right off the bat, have them help each other out, then of course they will see each piece over and over again as we work through lessons each day. Right now, however, with our first class day being on a Friday, this is my best guess of what I'd like to do with this day. I'm still debating whether this is a good idea, or whether I want to introduce one thing at a time over the course of a week or so, so feedback is appreciated.